Predicting permeability via statistical learning on higher-order microstructural information

Abstract

Quantitative structure–property relationships are crucial for the understanding and prediction of the physical properties of complex materials. For fluid flow in porous materials, characterizing the geometry of the pore microstructure facilitates prediction of permeability, a key property that has been extensively studied in material science, geophysics and chemical engineering. In this work, we study the predictability of different structural descriptors via both linear regressions and neural networks. A large data set of 30,000 virtual, porous microstructures of different types, including both granular and continuous solid phases, is created for this end. We compute permeabilities of these structures using the lattice Boltzmann method, and characterize the pore space geometry using one-point correlation functions (porosity, specific surface), two-point surface-surface, surface-void, and void-void correlation functions, as well as the geodesic tortuosity as an implicit descriptor. Then, we study the prediction of the permeability using different combinations of these descriptors. We obtain significant improvements of performance when compared to a Kozeny-Carman regression with only lowest-order descriptors (porosity and specific surface). We find that combining all three two-point correlation functions and tortuosity provides the best prediction of permeability, with the void-void correlation function being the most informative individual descriptor. Moreover, the combination of porosity, specific surface, and geodesic tortuosity provides very good predictive performance. This shows that higher-order correlation functions are extremely useful for forming a general model for predicting physical properties of complex materials. Additionally, our results suggest that artificial neural networks are superior to the more conventional regression methods for establishing quantitative structure–property relationships. We make the data and code used publicly available to facilitate further development of permeability prediction methods.

Prediction and Optimization of Ion Transport Characteristics in Nanoparticle-Based Electrolytes Using Convolutional Neural Networks

“…42 We also explored another surrogate model with nanoparticle-nanoparticle radial distribution function as the input feature to predict cation diffusivity. Although other two-point (particle-particle) correlation functions have been employed as structural descriptors for predicting properties of composites with granular and continuous phases, 24,31,32,[53][54][55][56][57][58][59] we observe the radial distribution functions to be a more relevant descriptor for the microstructures in our case with uniformly sized nanoparticles (supporting results in SI, Section S6.2). Further details on the architecture of the deep artificial neural networks adopted for the above physics-inspired approaches are provided in SI, Section S6.1.…”

“…In the studies pertaining to the former, the hand-crafted features representing the microstructure are linked to an associated property using a regression-based model [24][25][26][27][28][29][30] or artificial neural network. 31,32 For the latter case, convolutional neural networks (CNNs) 33 are employed to extract important features from the digitized images of composite microstructures, generated by stochastic growth of grains [34][35][36][37][38] or by random assignment of numbers in the uniformly voxelized grids, [39][40][41] in order to predict the effective property of interest. Motivated by the above advances, we hypothesize that machine learning techniques can be similarly applied to correlate the properties of nanocomposites reinforced with spherical nanoparticles to their microstructure.…”

Large-Scale Statistical Learning for Mass Transport Prediction in Porous Materials Using 90,000 Artificially Generated Microstructures

“…In Stenzel et al (2017), effective conductivity (mathematically equivalent to effective diffusivity) and numerous structural descriptors including constrictivity and tortuosity were computed for 8,119 microstructures, where conventional regression, random forests, and artificial neural networks (ANNs) were used for prediction. In Röding et al (2020), permeability, tortuosity and two-point correlation functions were computed for 30,000 structures, where log-linear regression and ANNs were used for prediction. Although machine learning regression using ANNs is less transparent compared to analytical prediction formulas and hence less interpretable, the benefit of this approach is that arbitrarily complex relationships can be represented by a feedforward network due to the universal approximation theorem (Cybenko, 1989;Hornik et al, 1989).…”

“…Although machine learning regression using ANNs is less transparent compared to analytical prediction formulas and hence less interpretable, the benefit of this approach is that arbitrarily complex relationships can be represented by a feedforward network due to the universal approximation theorem (Cybenko, 1989;Hornik et al, 1989). Hence, machine learning regression can be considered a data-science approach that leads to insight into new relationships and into which descriptors are most useful for prediction (Umehara et al, 2019;Röding et al, 2020). A third option is the prediction of effective properties using convolutional neural networks (CNNs).…”

Prediction and Optimization of Ion Transport Characteristics in Nanoparticle-Based Electrolytes Using Convolutional Neural Networks

“…In the studies pertaining to the former, the hand-crafted features representing the microstructure are linked to an associated property using a regression-based model [24][25][26][27][28][29][30] or artificial neural network. 31,32 For the latter case, convolutional neural networks (CNNs) 33 are employed to extract important features from the digitized images of composite microstructures, generated by stochastic growth of grains [34][35][36][37][38] or by random assignment of numbers in the uniformly voxelized grids, [39][40][41] in order to predict the effective property of interest. Motivated by the above advances, we hypothesize that machine learning techniques can be similarly applied to correlate the properties of nanocomposites reinforced with spherical nanoparticles to their microstructure.…”